### Abstract

Let R be a 2-torsion free commutative ring with involution *, and δ a non-zero derivation of R. Let S be the set of symmetric elements in R and K the set of anti-symmetric elements in R. In this article, we investigate the simplicity and primeness of the Lie rings Sδ and Kδ when δ is a symmetric or anti-symmetric derivation.

Original language | English |
---|---|

Pages (from-to) | 589-598 |

Number of pages | 10 |

Journal | Linear and Multilinear Algebra |

Volume | 58 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*58*(5), 589-598. https://doi.org/10.1080/03081080902765609

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*Linear and Multilinear Algebra*, vol. 58, no. 5, pp. 589-598. https://doi.org/10.1080/03081080902765609

**Lie rings of (anti-)symmetric derivations of commutative rings.** / Liao, Ping Bao; Liu, Cheng Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Lie rings of (anti-)symmetric derivations of commutative rings

AU - Liao, Ping Bao

AU - Liu, Cheng Kai

PY - 2010/7/1

Y1 - 2010/7/1

N2 - Let R be a 2-torsion free commutative ring with involution *, and δ a non-zero derivation of R. Let S be the set of symmetric elements in R and K the set of anti-symmetric elements in R. In this article, we investigate the simplicity and primeness of the Lie rings Sδ and Kδ when δ is a symmetric or anti-symmetric derivation.

AB - Let R be a 2-torsion free commutative ring with involution *, and δ a non-zero derivation of R. Let S be the set of symmetric elements in R and K the set of anti-symmetric elements in R. In this article, we investigate the simplicity and primeness of the Lie rings Sδ and Kδ when δ is a symmetric or anti-symmetric derivation.

UR - http://www.scopus.com/inward/record.url?scp=77954282340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954282340&partnerID=8YFLogxK

U2 - 10.1080/03081080902765609

DO - 10.1080/03081080902765609

M3 - Article

AN - SCOPUS:77954282340

VL - 58

SP - 589

EP - 598

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 5

ER -